Sequential Monte Carlo methods have been a major breakthrough in the field of numerical signal processing for stochastic dynamical state-space systems with partial and noisy observations. However, these methods still present certain weaknesses. One of the most fundamental is the degeneracy of the filter due to the impoverishment of the particles: the prediction step allows the particles to explore the state-space and can lead to the impoverishment of the particles if this exploration is poorly conducted or when it conflicts with the following observation that will be used in the evaluation of the likelihood of each particle. In this article, in order to improve this last step within the framework of the classic bootstrap particle filter, we propose a simple approximation of the one step fixed-lag smoother. At each time iteration, we propose to perform additional simulations during the prediction step in order to improve the likelihood of the selected particles.

翻译：序贯蒙特卡洛方法在具有部分噪声观测的随机动态状态空间系统的数值信号处理领域取得了重大突破。然而，这些方法仍存在某些缺陷。其中最根本的问题之一是粒子贫化导致的滤波退化：预测步骤允许粒子探索状态空间，若该探索执行不当或与后续用于评估各粒子似然的观测值产生冲突，则可能导致粒子贫化。本文针对经典自举粒子滤波框架，为改进最后一步提出了一种对单步固定滞后平滑器的简单近似。在每个时间迭代中，我们建议在预测步骤期间执行额外模拟，以提升所选粒子的似然度。